Error structure for split-split plot with treatment across blocks

-----Original Message-----
From: Elizabeth Graham [mailto:sharon.graham at pg.canterbury.ac.nz]
Sent: 21 October 2013 20:27
m2<-lme(log(density)~Treatment*Shade*Leaves,
                        random=~1|Stream/Shade/Leaves)

was actually my original model structure, but has the same incongruity
between model results and interaction plots - try
interaction.plot(Shade, Treatment, density) for an example - the
treatment and control lines do not intersect at all, and standard error
bars do not overlap.  

The default interaction.plot doesn't use the Stream random effect in its error bars; it's using the group means and standard errors based on assumed simple independent replication. Those 'replicates' aren't independent. That will tend to give underestimated standard errors compared to a correct nested random effects structure, as the Stream effect is quite big. 

S Ellison


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